arXiv 2201.072512022-01hep-phhep-exnucl-exnucl-th

用$^{151}{\rm \bf Sm}$和$^{171}{\rm \bf Tm}$探测宇宙中微子的经验俘获截面

Empirical capture cross sections for cosmic neutrino detection with $^{151}{\rm \bf Sm}$ and $^{171}{\rm \bf Tm}$

Vedran Brdar, Ryan Plestid, Noemi Rocco

备注：: published version; 10 pages, 2 figures
发表信息：: Phys. Rev. C 105, 045501 (2022)
DOI：: 10.1103/PhysRevC.105.045501

摘要：

核$^{151}$ Sm和$^{171}$ Tm已被确定为探测宇宙中微子背景的有吸引力的候选者。这两种同位素都经历了第一禁戒的非唯一β衰变，这抑制了单独使用对称性对其光谱形状的预测，到目前为止，这阻碍了对其中微子捕获截面的明确预测。在这项工作中，我们指出，对于这两个元素的所谓的“$ξ$近似”是适用的，这有效地减少了频谱形状偏离最多$1\%$从一个，如果β衰变是允许的类型。使用测量的半衰期，我们提取相关的核矩阵元素和预测的中微子捕获截面为两种同位素在$1\%$水平，占一些相关的影响，包括辐射校正和有限大小的核。我们得到了$^{171}$ Tm的$(1.12\pm 0.01)\times 10^{-46}{\rm cm}^2$和$^{151}$ Sm的$(4.77\pm 0.01)\times 10^{-48}{\rm cm}^2$。该方法是稳健的，因为它不依赖于可能被原子物理学效应（即，抖动和抖动）污染的β谱的终点附近的数据点。最后，我们计算了发现宇宙中微子所需的靶质量，并讨论了实验计划中的几个瓶颈和相应的解决方案。我们的结论是，宇宙中微子背景的探测中微子捕获$^{151}$ Sm和$^{171}$ Tm是可以实现的，没有理论上的限制，但仍然受到技术问题，应该进一步研究的背景下，拟议的PIMMY项目的实验。

英文摘要：

The nuclei $^{151}$Sm and $^{171}$Tm have been identified as attractive candidates for the detection of the cosmic neutrino background. Both isotopes undergo first-forbidden non-unique beta decays which inhibits a prediction of their spectral shape using symmetries alone and this has, so far, obstructed a definitive prediction of their neutrino capture cross sections. In this work we point out that for both elements the so-called "$ξ$-approximation" is applicable and this effectively reduces the spectral shape to deviate by at most $1\%$ from the one that would arise if beta decays were of the allowed type. Using measured half-lives we extract the relevant nuclear matrix element and predict the neutrino capture cross sections for both isotopes at $1\%$ level, accounting for a number of relevant effects including radiative corrections and the finite size of the nuclei. We obtained $(1.12\pm 0.01)\times 10^{-46}{\rm cm}^2$ for $^{171}$Tm and $(4.77\pm 0.01)\times 10^{-48}{\rm cm}^2$ for $^{151}$Sm. This method is robust as it does not rely on the data points near the end-point of the beta spectrum which may be contaminated by atomic physics effects, namely shake-up and shake-off. Finally, we calculate the target mass which is necessary for cosmic neutrino discovery and discuss several bottlenecks and respective solutions associated to the experimental program. We conclude that the detection of cosmic neutrino background by neutrino capture on $^{151}$Sm and $^{171}$Tm is achievable and free from theoretical limitations but still subject to technical issues that should be further investigated by the experimentalists in the context of the proposed PTOLEMY project.

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